4. Euclid Alone Has Looked on Beauty Bare (1)

I am poor at mathematics and
hate the subject but love it too much to leave it alone.I am more fascinated by the questions the
system raises than the answers it gives us.Mathematics can play a major role in our view of the world.The hubris of mathematicians may plainly be
seen in those who think that the final explanation of existence will be a mathematical
formula, attainable and perhaps even soon to be discovered.In one of my novels, a character asks of
another whether he would marry a complete mathematical model of a beloved woman.One supposes that something vital and real in
the woman would be missing from a mathematical model of her, no matter how
perfect and complete the defining math.Cleopatra
was something more than a rigid relationship among variables, which is a way of
saying that Nature is not a subset of Mathematics. Nevertheless, we cannot dismiss entirely the
possibility that a complete model of a human actually is that human.Our knowledge
of nature comes from a verifying science that always leaves room for doubt and
never escapes from degrees of probability rather than absolute certainty.

Abusive use of mathematics
occurs in the soft sciences that investigate complexities that cannot be
reduced to controlled experiments.Usually, the abuse takes the form of claiming valid inferences about
biological, environmental, or social phenomena but without data from controlled
experiments that make precise predictions about expected outcomes.Because I have spent thousands of hours
pursuing economic questions, I will illustrate the malpractice in that
context.Economists sometimes call their
trade the Queen of the Social Sciences because it is so highly
mathematized.That chutzpah covers a
major case of pseudo physics.

Usually it surprises the
novice to find that economists are as mathematical as physicists, in some ways
more so.Anyone even slightly familiar
with the forays since the 1970s into string theory may doubt that economists
reach similar mathematical altitudes.I
have in mind, however, the peculiar fact that the passion of the physicist is
directed toward nature itself.Economists
instead often suffer tools gladly.In
most undergraduate texts, we would notice only as elementary algebra, some
forays into marginals, or perhaps some calculus footnotes.Beyond these first encounters, economic
theories reside in a thicket of mathematics, much of it thorny.Further, the profession itself, as seen in
its journals and awards, operates through its mathematicians at surprising
levels of abstraction and formalism.The
dominant and dominating economists wield mathematics like a scepter.Even the profession’s policy pundits must
either pass a mathematical litmus test in the journals or be looked down upon.

Why the
mathematical Mandarins?Let me tell you
a story.Once I was taking a French
literature class in which our session always followed a physics lecture in the
same room.One morning the physicist was
running late.After we had filed in,
suddenly he set to, erasing the blackboard equations furiously as though in
great alarm.Then that gentleman, who
spoke French comme une vache, turned to us with a grin and explained
that he had not wanted to frighten us.So saying, he airily left the room, leaving us humble folk to turn our
attention to Molière.

Thereby hangs at
least half the tale of modern economics. Even so, thought experiments are
reasonable activity.These do contain
insights, sometimes deep ones.Therefore, unlike Whitman, we do not abandon the learned astronomer in
his lecture hall to go out into the mystical moist night air and look up in
perfect silence at the stars.Our caveat
concerning even the best of pure structures is that they can be critically
misleading if taken physically.The
profession’s scholasticism has numerous devices imprecisely similar to the
point particles (of zero dimensions) in particle physics, which is an
idealization that has its uses but has led to absurdities.It is “imprecisely similar” because, in
physics, theory is either heading for the laboratory or else heading out the
door.Among economists, pure theory is
the man who came to dinner.

Setting aside the abuses of
mathematics, what can we do with it when we use it validly?What does it tell us about love, about our
minds and our emotions, about suicide, about hatreds and other passions or
about the celebrated quiet desperation of most lives?Nothing.Nothing at all. It helps us to keep our airplanes flying, our
ships afloat.It enhances our control of
the environment around us and is part of our cunning and even of our safety.It whispers to us prophetically, like
Cassandra herself, of the cogs and wheels in the great machine around us.It tells us nothing of the ghost in the
machine.As a romantic, I find the
greatest thing about mathematics, the priceless gift that it give us, comes
from the radiant beauty that lurks like a whispering angel among the equations
and topologies.It holds within itself the
most beautiful things mere humans ever encounter.Euclid alone has looked on beauty bare and
heard her massive sandal set on stone.